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      <h1 id="数据结构-01-堆和二叉堆"><a href="#数据结构-01-堆和二叉堆" class="headerlink" title="数据结构-01-堆和二叉堆"></a>数据结构-01-堆和二叉堆</h1><p>参考博客 ： <a href="https://www.cnblogs.com/skywang12345/p/3603935.html" target="_blank" rel="noopener">https://www.cnblogs.com/skywang12345/p/3603935.html</a></p>
<p>本章介绍二叉堆，二叉堆就是通常我们所说的数据结构中”堆”中的一种。</p>
<a id="more"></a>



<h2 id="1-堆的定义"><a href="#1-堆的定义" class="headerlink" title="1. 堆的定义"></a>1. 堆的定义</h2><ul>
<li><p>堆（heap） ，这里所说的堆是数据结构中的堆，而不是内存模型中的堆。</p>
</li>
<li><p><strong>堆通常可以被看做一棵树，它满足以下性质</strong></p>
<ul>
<li><strong>堆中任意节点的值总是不大于（不小于）其子节点的值</strong></li>
<li><strong>堆总是一个完全树</strong></li>
</ul>
</li>
<li><p>将任意节点不大于其子节点的堆叫做最小堆或小根堆</p>
</li>
<li><p>将任意节点不小于其子节点的堆叫做最大堆或大根堆</p>
</li>
</ul>
<p>常见的堆有二叉堆、左倾堆、斜堆、二项堆、斐波那契堆等等。</p>
<h2 id="2-二叉堆的定义"><a href="#2-二叉堆的定义" class="headerlink" title="2. 二叉堆的定义"></a>2. 二叉堆的定义</h2><p>二叉堆是完全二元树或者是近似完全二元树，它分为两种：最大堆和最小堆。</p>
<ul>
<li>最大堆：父节点的键值总是大于或者等于任何一个子节点的键值。</li>
<li>最小堆：父结点的键值总是小于或等于任何一个子节点的键值。</li>
</ul>
<p>示意图如下：</p>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/110858045.png" alt="mark"></p>
<p>二叉堆一般都是通过<strong>数组</strong>来实现。数组实现的二叉堆，父节点和子节点的位置存在一定的关系。</p>
<ul>
<li>有时候，我们将”二叉堆的第一个元素”放在数组索引 0 的位置，有时候放在1的位置。当然，他们的本质一样（都是二叉堆），只是实现上稍微有一丁点区别</li>
<li><strong>假设”第一个元素”在数组中的索引为 0 的话</strong>，则父节点和子节点的位置关系如下：<ul>
<li>索引为i的左孩子的索引是 <code>（2i+1);</code></li>
<li>索引为i的左孩子的索引是  <code>(2i+2);</code></li>
<li>索引为i的父节点索引是<code>floor((i-1)/2);</code></li>
</ul>
</li>
</ul>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/113301481.png" alt="mark"></p>
<ul>
<li>假设”第一个元素”在数组中的索引为 1 的话，则父节点和子节点的位置关系如下：<ul>
<li>索引为i的左孩子的索引是 <code>(2i);</code></li>
<li>索引为i的左孩子的索引是 <code>(2i+1);</code></li>
<li>索引为i的父结点的索引是<code>floor(i/2);</code></li>
</ul>
</li>
</ul>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/115323001.png" alt="mark"></p>
<p><strong>注意：本文二叉堆的实现统统都是采用”二叉堆第一个元素在数组索引为0”的方式！</strong></p>
<h2 id="3-二叉堆的图文解析"><a href="#3-二叉堆的图文解析" class="headerlink" title="3. 二叉堆的图文解析"></a>3. 二叉堆的图文解析</h2><p>在前面，我们已经了解到：”最大堆”和”最小堆”是对称关系。这也意味着，了解其中之一即可。本节的图文解析是以”最大堆”来进行介绍的。</p>
<p>二叉堆的核心是“添加节点”和“删除节点”，理解这两个算法，二叉堆也就基本掌握了。下面对它们进行介绍。</p>
<h3 id="3-1-添加"><a href="#3-1-添加" class="headerlink" title="3.1 添加"></a>3.1 添加</h3><p>假设在<strong>最大堆</strong><code>[90,80,70,60,40,30,20,10,50]</code>种添加85，需要执行的步骤如下：</p>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/120036286.png" alt="mark"></p>
<p>如上图所示，当向最大堆中添加数据时候；先将数据加入到最大堆的最后，然后尽可能把这个元素向上挪，直到挪不动位置。</p>
<p>将85添加到[90,80,70,60,40,30,20,10,50]中后，最大堆变成了[90,85,70,60,80,30,20,10,50,40]。</p>
<p><strong>最大堆的插入代码(Java语言)</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 最大堆的向上调整算法(从start开始向上直到0，调整堆)</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 参数说明：</span></span><br><span class="line"><span class="comment"> *     start -- 被上调节点的起始位置(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterup</span><span class="params">(<span class="keyword">int</span> start)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> c = start;            <span class="comment">// 当前节点(current)的位置</span></span><br><span class="line">    <span class="keyword">int</span> p = (c-<span class="number">1</span>)/<span class="number">2</span>;          <span class="comment">// 父(parent)结点的位置 </span></span><br><span class="line">    T tmp = mHeap.get(c);     <span class="comment">// 当前节点(current)的大小</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span>(c &gt; <span class="number">0</span>) &#123;</span><br><span class="line">        <span class="keyword">int</span> cmp = mHeap.get(p).compareTo(tmp);</span><br><span class="line">        <span class="keyword">if</span>(cmp &gt;= <span class="number">0</span>)</span><br><span class="line">            <span class="keyword">break</span>;</span><br><span class="line">        <span class="keyword">else</span> &#123;</span><br><span class="line">            mHeap.set(c, mHeap.get(p));</span><br><span class="line">            c = p;</span><br><span class="line">            p = (p-<span class="number">1</span>)/<span class="number">2</span>;   </span><br><span class="line">        &#125;       </span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 最后再把值换上去</span></span><br><span class="line">    mHeap.set(c, tmp);</span><br><span class="line">&#125;</span><br><span class="line">  </span><br><span class="line"><span class="comment">/* </span></span><br><span class="line"><span class="comment"> * 将data插入到二叉堆中</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">insert</span><span class="params">(T data)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line"></span><br><span class="line">    mHeap.add(data);     <span class="comment">// 将"数组"插在表尾</span></span><br><span class="line">    filterup(size);        <span class="comment">// 向上调整堆</span></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>







<h3 id="3-2-删除"><a href="#3-2-删除" class="headerlink" title="3.2 删除"></a>3.2 删除</h3><p><code>假设从最大堆[90,85,70,60,80,30,20,10,50,40]中删除90，需要执行的步骤如下：</code></p>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/120626872.png" alt="mark"></p>
<p><code>从[90,85,70,60,80,30,20,10,50,40]删除90之后，最大堆变成了[85,80,70,60,40,30,20,10,50]。</code></p>
<p>如上图所示，当从最大堆中删除数据时候；</p>
<ul>
<li>先删除该数据，然后用最大堆中的最后一个元素插入这个空位。</li>
<li>接着，把这个空位尽量向下挪，直到剩余数据变成一个最大堆。</li>
</ul>
<p><strong>注意：考虑从最大堆[90,85,70,60,80,30,20,10,50,40]中删除60，执行的步骤不能单纯的用它的子节点来替换；而必须考虑到”替换后的树仍然要是最大堆”！</strong></p>
<p><img src="http://zhuuu-bucket.oss-cn-beijing.aliyuncs.com/img/20200603/120823590.png" alt="mark"></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/* </span></span><br><span class="line"><span class="comment"> * 最大堆的向下调整算法</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 参数说明：</span></span><br><span class="line"><span class="comment"> *     start -- 被下调节点的起始位置(一般为0，表示从第1个开始)</span></span><br><span class="line"><span class="comment"> *     end   -- 截至范围(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterdown</span><span class="params">(<span class="keyword">int</span> start, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> c = start;          <span class="comment">// 当前(current)节点的位置</span></span><br><span class="line">    <span class="keyword">int</span> l = <span class="number">2</span>*c + <span class="number">1</span>;     <span class="comment">// 左(left)孩子的位置</span></span><br><span class="line">    T tmp = mHeap.get(c);    <span class="comment">// 当前(current)节点的大小</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span>(l &lt;= end) &#123;</span><br><span class="line">        <span class="keyword">int</span> cmp = mHeap.get(l).compareTo(mHeap.get(l+<span class="number">1</span>));</span><br><span class="line">        <span class="comment">// "l"是左孩子，"l+1"是右孩子</span></span><br><span class="line">        <span class="keyword">if</span>(l &lt; end &amp;&amp; cmp&lt;<span class="number">0</span>)</span><br><span class="line">            l++;        <span class="comment">// 左右两孩子中选择较大者，即mHeap[l+1]</span></span><br><span class="line">        cmp = tmp.compareTo(mHeap.get(l));</span><br><span class="line">        <span class="keyword">if</span>(cmp &gt;= <span class="number">0</span>)</span><br><span class="line">            <span class="keyword">break</span>;        <span class="comment">//调整结束</span></span><br><span class="line">        <span class="keyword">else</span> &#123;</span><br><span class="line">            mHeap.set(c, mHeap.get(l));</span><br><span class="line">            c = l;</span><br><span class="line">            l = <span class="number">2</span>*l + <span class="number">1</span>;   </span><br><span class="line">        &#125;       </span><br><span class="line">    &#125;   </span><br><span class="line">    mHeap.set(c, tmp);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 删除最大堆中的data</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 返回值：</span></span><br><span class="line"><span class="comment"> *      0，成功</span></span><br><span class="line"><span class="comment"> *     -1，失败</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">remove</span><span class="params">(T data)</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 如果"堆"已空，则返回-1</span></span><br><span class="line">    <span class="keyword">if</span>(mHeap.isEmpty() == <span class="keyword">true</span>)</span><br><span class="line">        <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 获取data在数组中的索引</span></span><br><span class="line">    <span class="keyword">int</span> index = mHeap.indexOf(data);</span><br><span class="line">    <span class="keyword">if</span> (index==-<span class="number">1</span>)</span><br><span class="line">        <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line">    mHeap.set(index, mHeap.get(size - <span class="number">1</span>));   <span class="comment">// 用最后元素填补</span></span><br><span class="line">    mHeap.remove(size - <span class="number">1</span>);                <span class="comment">// 删除最后的元素</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (mHeap.size() &gt; <span class="number">1</span>)</span><br><span class="line">        filterdown(index, mHeap.size()-<span class="number">1</span>);    <span class="comment">// 从index号位置开始自上向下调整为最大堆</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>



<h2 id="4-完整源码"><a href="#4-完整源码" class="headerlink" title="4. 完整源码"></a>4. 完整源码</h2><ul>
<li>最大堆的实现（MaxHeap.java）</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">package</span> Heap;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 二叉堆(最大堆) 实现</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">import</span> java.util.ArrayList;</span><br><span class="line"><span class="keyword">import</span> java.util.List;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">MaxHeap</span> &lt;<span class="title">T</span> <span class="keyword">extends</span> <span class="title">Comparable</span>&lt;<span class="title">T</span>&gt;&gt;</span>&#123;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">private</span> List&lt;T&gt; mHeap;    <span class="comment">// 队列(实际上是动态数组ArrayList的实例)</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="title">MaxHeap</span><span class="params">()</span></span>&#123;</span><br><span class="line">        <span class="keyword">this</span>.mHeap = <span class="keyword">new</span> ArrayList&lt;T&gt;();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">     * 最大堆的向下调整算法</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 参数说明：</span></span><br><span class="line"><span class="comment">     *     start -- 被下调节点的起始位置(一般为0，表示从第1个开始)</span></span><br><span class="line"><span class="comment">     *     end   -- 截至范围(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterdown</span><span class="params">(<span class="keyword">int</span> start,<span class="keyword">int</span> end)</span></span>&#123;</span><br><span class="line">        <span class="keyword">int</span> c = start;       <span class="comment">// 当前节点的位置</span></span><br><span class="line">        <span class="keyword">int</span> l = <span class="number">2</span>*c + <span class="number">1</span>;     <span class="comment">// 左孩子的位置</span></span><br><span class="line">        T tmp = mHeap.get(c);<span class="comment">// 当前节点的大小</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (l &lt;= end)&#123;</span><br><span class="line">            <span class="keyword">int</span> cmp = mHeap.get(l).compareTo(mHeap.get(l + <span class="number">1</span>));</span><br><span class="line">            <span class="comment">// "l"是左孩子，"l+1"是右孩子</span></span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (l &lt; end &amp;&amp; cmp &lt; <span class="number">0</span>)&#123;</span><br><span class="line">                l ++;   <span class="comment">// 左右两孩子中选择较大者，即mHeap[l+1]</span></span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">            cmp = tmp.compareTo(mHeap.get(l));</span><br><span class="line">            <span class="keyword">if</span> (cmp &gt;= <span class="number">0</span>)&#123;</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">            &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">                mHeap.set(c,mHeap.get(l));  <span class="comment">// 用数组最后一个元素放到该位置</span></span><br><span class="line">                c = l;              <span class="comment">// 索引变为其父节点</span></span><br><span class="line">                l = <span class="number">2</span>*l + <span class="number">1</span>;        <span class="comment">// 父节点变为原子节点</span></span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        mHeap.set(c,tmp);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">    * 删除最大堆中的data</span></span><br><span class="line"><span class="comment">    *</span></span><br><span class="line"><span class="comment">    * 返回值：</span></span><br><span class="line"><span class="comment">    *      0，成功</span></span><br><span class="line"><span class="comment">    *     -1，失败</span></span><br><span class="line"><span class="comment">    */</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">remove</span><span class="params">(T data)</span></span>&#123;</span><br><span class="line">    <span class="comment">// 如果"堆"已空，则返回-1</span></span><br><span class="line">        <span class="keyword">if</span>(mHeap.isEmpty() == <span class="keyword">true</span>)&#123;</span><br><span class="line">            <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 获取data在数组中的索引</span></span><br><span class="line">        <span class="keyword">int</span> index = mHeap.indexOf(data);</span><br><span class="line">        <span class="keyword">if</span> (index==-<span class="number">1</span>)&#123;</span><br><span class="line">            <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line">        mHeap.set(index, mHeap.get(size-<span class="number">1</span>));    <span class="comment">// 用最后元素填补</span></span><br><span class="line">        mHeap.remove(size - <span class="number">1</span>);           <span class="comment">// 删除最后的元素</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (mHeap.size() &gt; <span class="number">1</span>) &#123;</span><br><span class="line">            filterdown(index, mHeap.size()-<span class="number">1</span>);    <span class="comment">// 从index号位置开始自上向下调整为最小堆</span></span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 最大堆的向上调整算法(从start开始向上直到0，调整堆)</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * 参数说明：</span></span><br><span class="line"><span class="comment"> *     start -- 被上调节点的起始位置(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterup</span><span class="params">(<span class="keyword">int</span> start)</span></span>&#123;</span><br><span class="line">        <span class="keyword">int</span> c = start;          <span class="comment">// 当前节点的位置</span></span><br><span class="line">        <span class="keyword">int</span> p = (c - <span class="number">1</span>)/<span class="number">2</span>;      <span class="comment">// 父节点的位置</span></span><br><span class="line">        T tmp = mHeap.get(c);   <span class="comment">// 当前索引对应的值</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (c &gt; <span class="number">0</span>)&#123;</span><br><span class="line">            <span class="keyword">int</span> cmp = mHeap.get(p).compareTo(tmp);</span><br><span class="line">            <span class="keyword">if</span> (cmp &gt;= <span class="number">0</span>)&#123;</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">            &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">                mHeap.set(c,mHeap.get(p));</span><br><span class="line">                c = p;</span><br><span class="line">                p = (p - <span class="number">1</span>)/<span class="number">2</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        mHeap.set(c,tmp);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">/**</span></span><br><span class="line"><span class="comment">     * 将data插入到二叉堆中</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">insert</span><span class="params">(T data)</span></span>&#123;</span><br><span class="line">        <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line"></span><br><span class="line">        mHeap.add(data);  <span class="comment">// 首先将元素插到数组末尾</span></span><br><span class="line">        filterup(size);    <span class="comment">// 向上调整堆</span></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> String <span class="title">toString</span><span class="params">()</span></span>&#123;</span><br><span class="line">        StringBuilder sb = <span class="keyword">new</span> StringBuilder();</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; mHeap.size(); i++) &#123;</span><br><span class="line">            sb.append(mHeap.get(i) + <span class="string">" "</span>);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> sb.toString();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 测试用例</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> i;</span><br><span class="line">        <span class="keyword">int</span> a[] = &#123;<span class="number">10</span>, <span class="number">40</span>, <span class="number">30</span>, <span class="number">60</span>, <span class="number">90</span>, <span class="number">70</span>, <span class="number">20</span>, <span class="number">50</span>, <span class="number">80</span>&#125;;</span><br><span class="line">        MaxHeap&lt;Integer&gt; tree = <span class="keyword">new</span> MaxHeap&lt;Integer&gt;();</span><br><span class="line"></span><br><span class="line">        System.out.printf(<span class="string">"== 依次添加: "</span>);</span><br><span class="line">        <span class="keyword">for</span>(i = <span class="number">0</span>; i &lt; a.length; i++) &#123;</span><br><span class="line">            System.out.printf(<span class="string">"%d "</span>, a[i]);</span><br><span class="line">            tree.insert(a[i]);</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 大 堆: %s"</span>, tree);</span><br><span class="line"></span><br><span class="line">        i=<span class="number">85</span>;</span><br><span class="line">        tree.insert(i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 添加元素: %d"</span>, i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 大 堆: %s"</span>, tree);</span><br><span class="line"></span><br><span class="line">        i=<span class="number">90</span>;</span><br><span class="line">        tree.remove(i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 删除元素: %d"</span>, i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 大 堆: %s"</span>, tree);</span><br><span class="line">        System.out.printf(<span class="string">"\n"</span>);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>



<ul>
<li>最小堆的实现</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">package</span> Heap;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 二叉堆(最小堆)</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">import</span> java.util.ArrayList;</span><br><span class="line"><span class="keyword">import</span> java.util.List;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">MinHeap</span>&lt;<span class="title">T</span> <span class="keyword">extends</span> <span class="title">Comparable</span>&lt;<span class="title">T</span>&gt;&gt; </span>&#123;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">private</span> List&lt;T&gt; mHeap;        <span class="comment">// 存放堆的数组</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="title">MinHeap</span><span class="params">()</span> </span>&#123;</span><br><span class="line">        <span class="keyword">this</span>.mHeap = <span class="keyword">new</span> ArrayList&lt;T&gt;();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">     * 最小堆的向下调整算法</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 参数说明：</span></span><br><span class="line"><span class="comment">     *     start -- 被下调节点的起始位置(一般为0，表示从第1个开始)</span></span><br><span class="line"><span class="comment">     *     end   -- 截至范围(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterdown</span><span class="params">(<span class="keyword">int</span> start, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> c = start;          <span class="comment">// 当前(current)节点的位置</span></span><br><span class="line">        <span class="keyword">int</span> l = <span class="number">2</span>*c + <span class="number">1</span>;     	<span class="comment">// 左(left)孩子的位置</span></span><br><span class="line">        T tmp = mHeap.get(c);    <span class="comment">// 当前(current)节点的大小</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span>(l &lt;= end) &#123;</span><br><span class="line">            <span class="keyword">int</span> cmp = mHeap.get(l).compareTo(mHeap.get(l+<span class="number">1</span>));</span><br><span class="line">            <span class="comment">// "l"是左孩子，"l+1"是右孩子</span></span><br><span class="line">            <span class="keyword">if</span>(l &lt; end &amp;&amp; cmp&gt;<span class="number">0</span>)</span><br><span class="line">                l++;        <span class="comment">// 左右两孩子中选择较小者，即mHeap[l+1]</span></span><br><span class="line"></span><br><span class="line">            cmp = tmp.compareTo(mHeap.get(l));</span><br><span class="line">            <span class="keyword">if</span>(cmp &lt;= <span class="number">0</span>)</span><br><span class="line">                <span class="keyword">break</span>;        <span class="comment">//调整结束</span></span><br><span class="line">            <span class="keyword">else</span> &#123;</span><br><span class="line">                mHeap.set(c, mHeap.get(l));</span><br><span class="line">                c = l;</span><br><span class="line">                l = <span class="number">2</span>*l + <span class="number">1</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        mHeap.set(c, tmp);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">     * 最小堆的删除</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 返回值：</span></span><br><span class="line"><span class="comment">     *     成功，返回被删除的值</span></span><br><span class="line"><span class="comment">     *     失败，返回null</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">remove</span><span class="params">(T data)</span> </span>&#123;</span><br><span class="line">        <span class="comment">// 如果"堆"已空，则返回-1</span></span><br><span class="line">        <span class="keyword">if</span>(mHeap.isEmpty() == <span class="keyword">true</span>)</span><br><span class="line">            <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 获取data在数组中的索引</span></span><br><span class="line">        <span class="keyword">int</span> index = mHeap.indexOf(data);</span><br><span class="line">        <span class="keyword">if</span> (index==-<span class="number">1</span>)</span><br><span class="line">            <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line">        mHeap.set(index, mHeap.get(size-<span class="number">1</span>));   <span class="comment">// 用最后元素填补</span></span><br><span class="line">        mHeap.remove(size - <span class="number">1</span>);                <span class="comment">// 删除最后的元素</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (mHeap.size() &gt; <span class="number">1</span>)</span><br><span class="line">            filterdown(index, mHeap.size() - <span class="number">1</span>);    <span class="comment">// 从index号位置开始自上向下调整为最小堆</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">     * 最小堆的向上调整算法(从start开始向上直到0，调整堆)</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 注：数组实现的堆中，第N个节点的左孩子的索引值是(2N+1)，右孩子的索引是(2N+2)。</span></span><br><span class="line"><span class="comment">     *</span></span><br><span class="line"><span class="comment">     * 参数说明：</span></span><br><span class="line"><span class="comment">     *     start -- 被上调节点的起始位置(一般为数组中最后一个元素的索引)</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="function"><span class="keyword">protected</span> <span class="keyword">void</span> <span class="title">filterup</span><span class="params">(<span class="keyword">int</span> start)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> c = start;            <span class="comment">// 当前节点(current)的位置</span></span><br><span class="line">        <span class="keyword">int</span> p = (c-<span class="number">1</span>)/<span class="number">2</span>;          <span class="comment">// 父(parent)结点的位置</span></span><br><span class="line">        T tmp = mHeap.get(c);     <span class="comment">// 当前节点(current)的大小</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span>(c &gt; <span class="number">0</span>) &#123;</span><br><span class="line">            <span class="keyword">int</span> cmp = mHeap.get(p).compareTo(tmp);</span><br><span class="line">            <span class="keyword">if</span>(cmp &lt;= <span class="number">0</span>)</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">            <span class="keyword">else</span> &#123;</span><br><span class="line">                mHeap.set(c, mHeap.get(p));</span><br><span class="line">                c = p;</span><br><span class="line">                p = (p-<span class="number">1</span>)/<span class="number">2</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 最后再把值换上去</span></span><br><span class="line">        mHeap.set(c, tmp);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">/*</span></span><br><span class="line"><span class="comment">     * 将data插入到二叉堆中</span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">insert</span><span class="params">(T data)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> size = mHeap.size();</span><br><span class="line"></span><br><span class="line">        mHeap.add(data);       <span class="comment">// 将"数组"插在表尾</span></span><br><span class="line">        filterup(size);        <span class="comment">// 向上调整堆</span></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> String <span class="title">toString</span><span class="params">()</span> </span>&#123;</span><br><span class="line">        StringBuilder sb = <span class="keyword">new</span> StringBuilder();</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> i=<span class="number">0</span>; i&lt;mHeap.size(); i++)</span><br><span class="line">            sb.append(mHeap.get(i) +<span class="string">" "</span>);</span><br><span class="line"></span><br><span class="line">        <span class="keyword">return</span> sb.toString();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> i;</span><br><span class="line">        <span class="keyword">int</span> a[] = &#123;<span class="number">80</span>, <span class="number">40</span>, <span class="number">30</span>, <span class="number">60</span>, <span class="number">90</span>, <span class="number">70</span>, <span class="number">10</span>, <span class="number">50</span>, <span class="number">20</span>&#125;;</span><br><span class="line">        MinHeap&lt;Integer&gt; tree=<span class="keyword">new</span> MinHeap&lt;Integer&gt;();</span><br><span class="line"></span><br><span class="line">        System.out.printf(<span class="string">"== 依次添加: "</span>);</span><br><span class="line">        <span class="keyword">for</span>(i=<span class="number">0</span>; i&lt;a.length; i++) &#123;</span><br><span class="line">            System.out.printf(<span class="string">"%d "</span>, a[i]);</span><br><span class="line">            tree.insert(a[i]);</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 小 堆: %s"</span>, tree);</span><br><span class="line"></span><br><span class="line">        i=<span class="number">15</span>;</span><br><span class="line">        tree.insert(i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 添加元素: %d"</span>, i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 小 堆: %s"</span>, tree);</span><br><span class="line"></span><br><span class="line">        i=<span class="number">10</span>;</span><br><span class="line">        tree.remove(i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 删除元素: %d"</span>, i);</span><br><span class="line">        System.out.printf(<span class="string">"\n== 最 小 堆: %s"</span>, tree);</span><br><span class="line">        System.out.printf(<span class="string">"\n"</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>



<p>运行结果：</p>
<ul>
<li>最大堆(MaxHeap.java)的运行结果：</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line">== 依次添加: <span class="number">10</span> <span class="number">40</span> <span class="number">30</span> <span class="number">60</span> <span class="number">90</span> <span class="number">70</span> <span class="number">20</span> <span class="number">50</span> <span class="number">80</span> </span><br><span class="line">== 最 大 堆: <span class="number">90</span> <span class="number">80</span> <span class="number">70</span> <span class="number">60</span> <span class="number">40</span> <span class="number">30</span> <span class="number">20</span> <span class="number">10</span> <span class="number">50</span> </span><br><span class="line">== 添加元素: <span class="number">85</span></span><br><span class="line">== 最 大 堆: <span class="number">90</span> <span class="number">85</span> <span class="number">70</span> <span class="number">60</span> <span class="number">80</span> <span class="number">30</span> <span class="number">20</span> <span class="number">10</span> <span class="number">50</span> <span class="number">40</span> </span><br><span class="line">== 删除元素: <span class="number">90</span></span><br><span class="line">== 最 大 堆: <span class="number">85</span> <span class="number">80</span> <span class="number">70</span> <span class="number">60</span> <span class="number">40</span> <span class="number">30</span> <span class="number">20</span> <span class="number">10</span> <span class="number">50</span></span><br></pre></td></tr></table></figure>



<ul>
<li>最小堆(MinHeap.java)的运行结果：</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line">== 最 小 堆: <span class="number">10</span> <span class="number">20</span> <span class="number">30</span> <span class="number">50</span> <span class="number">90</span> <span class="number">70</span> <span class="number">40</span> <span class="number">80</span> <span class="number">60</span> </span><br><span class="line">== 添加元素: <span class="number">15</span></span><br><span class="line">== 最 小 堆: <span class="number">10</span> <span class="number">15</span> <span class="number">30</span> <span class="number">50</span> <span class="number">20</span> <span class="number">70</span> <span class="number">40</span> <span class="number">80</span> <span class="number">60</span> <span class="number">90</span> </span><br><span class="line">== 删除元素: <span class="number">10</span></span><br><span class="line">== 最 小 堆: <span class="number">15</span> <span class="number">20</span> <span class="number">30</span> <span class="number">50</span> <span class="number">90</span> <span class="number">70</span> <span class="number">40</span> <span class="number">80</span> <span class="number">60</span></span><br></pre></td></tr></table></figure>


      
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